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Re: R: R: Help.Help.Help.Help

• To: mathgroup at smc.vnet.net
• Subject: [mg15372] Re: [mg15333] R: R: Help.Help.Help.Help
• From: Jurgen Tischer <jtischer at col2.telecom.com.co>
• Date: Sat, 9 Jan 1999 23:58:26 -0500
• Organization: Universidad del Valle
• References: <199901080915.EAA04012@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

Alessandro,
not having your files I had to improvise, copy the cells below in a
notebook and evaluate, maybe it's what you want. (If you have limited
memory you might want to reduce the animations.)

Notebook[{

Cell[CellGroupData[{
Cell["circle trayectory", "Subsubsection"],

Cell[BoxData[
    \(circ[n_] := 
      Table[N[{\(-1\), 1} +  .3 {Cos[f], Sin[f]}], {f, 0, 2  \[Pi], 
          \(2  \[Pi]\)\/n}]\)], "Input"],

Cell[BoxData[
    \(\(c[t_] = 
      \({x[t], y[t]} /. 
            \(NDSolve[{\(x'\)[t] == y[t], 
                  \(y'\)[t] == Cos[t] - y[t] - x[t]\^3, x[0] ==
#[\([1]\)], 
                  y[0] == #[\([2]\)]}, {x, y}, {t, 0,
10}]\)[\([1]\)]&\)/@
        circ[100]; \)\)], "Input"],

Cell[BoxData[
    \(Do[ListPlot[c[n], AspectRatio -> Automatic, PlotJoined -> True, 
        PlotRange -> {{\(-1.5\), 1}, {\(-1\), 1.5}}], {n, 0, 10, 
.1}]\)], 
  "Input"],

Cell[BoxData[
    \(Do[ListPlot[c[n], AspectRatio -> Automatic, PlotJoined -> True],
{n, 0, 
        10,  .1}]\)], "Input"]
}, Open  ]]
},
FrontEndVersion->"Microsoft Windows 3.0", ScreenRectangle->{{0, 1024},
{0, 740}}, WindowToolbars->"EditBar",
WindowSize->{496, 602},
WindowMargins->{{10, Automatic}, {Automatic, 15}} ]

Jurgen


Alessandro Ercolani wrote:
> 
> [Contact the author to obtain the file mentioned below - moderator]
> 
> Hi
> It's me Alessandro Ercolani.
> I'd like to explain well my problem. The file Duff1.bmp is token from
> file orbits.nb. It show the evolution of circle of initial condition of
> radius r that it follow the Duffing's equation
> x''[t]+x'[t]+(x[t]^3)==Cos[t] I thought to put together Duffin's
> equation and equation of a circle to calculate parametric equation of
> the curve in the picture for every t.  But using Mathematica 3.0 I have
> a lot of problems. A important thing is that the evolution of the
> Duffing's equation is represented on phase plane so on the axes there
> are x[t] and x'[t]. So for example the circle's equation is (x[t]^2) +
> (x' [t]^2) + ax[t]+bx' [t]+c==0
> Beside I don't have the exact initial conditions because x[0] and x'[0]
> don't represent a point but a circle. The only things that I know they
> are the center (-1,1) and the radius r=0.3 Can you help me please?
> Thanks in advance.

• References:
  • R: R: Help.Help.Help.Help
    • From: "Alessandro Ercolani" <alerco@tin.it>